Give domain and range if the graph of f(x)=-3/x-1+5

Answer 1

Hi Rudy O.,

For f(x) = -3/(x-1) + 5, x ≠ 1, so the domain is D: {x| x ≠ 1} or (-∞, 1)U(1, ∞).

For the domain we have an asymptote at x = 1.

As x goes to -∞ or +∞, -3/(x-1) goes to 0 and f(x) goes to 5. We can see this by exchanging y for x and x for y and solving for y:

x = -3/(y-1) + 5

x - 5 = -3/(y-1)

y-1 = -3/(x-5)

y = -3/(x-5) +1

So x ≠ 5, and the Range is R: {y| y ≠ 5} or (-∞, 5)U(5, ∞).

I hope this helps, Joe.